Question

请帮忙解一下方程，谢谢！

7x-5=50

若以下回答无法解决问题，邀请你更新回答

Answer 1

dt/dx = -cost
dt/cost = -dx
sect dt = - dx
∫sectdt
=∫dt/cost
=∫costdt/cos²t
=∫dsint/cos²t
=∫dsint/(1-sin²t)
=(1/2)[∫dsint/(sint+1)-∫dsint/(sint-1)]
=(1/2)(ln|sint+1|-ln|sint-1|)+C
=(1/2)ln|(sint+1)/(sint-1)|+C (对数里分子分母都乘以sint+1)
=(1/2)ln|(sint+1)²/cos²t|+C
=ln|(sint+1)/cost|+C
=ln|tant+sect|+C
所以
ln|tant+sect|=-x+C1
tant+sect=Ce^(-x)
所以tan(y-x)+sec(y-x)=Ce^(-x)